Question: $J$ $K$ $L$ If: $ JL = 111$, $ JK = 6x + 9$, and $ KL = 5x + 3$, Find $KL$.
Solution: From the diagram, we can see that the total length of ${JL}$ is the sum of ${JK}$ and ${KL}$ $ {JK} + {KL} = {JL}$ Substitute in the expressions that were given for each length: $ {6x + 9} + {5x + 3} = {111}$ Combine like terms: $ 11x + 12 = {111}$ Subtract $12$ from both sides: $ 11x = 99$ Divide both sides by $11$ to find $x$ $ x = 9$ Substitute $9$ for $x$ in the expression that was given for $KL$ $ KL = 5({9}) + 3$ Simplify: $ {KL = 45 + 3}$ Simplify to find ${KL}$ : $ {KL = 48}$